Saudi Arabia will not change its oil production policy in the short term despite the death of King Abdullah, Again Capital partner John Kilduff and other experts told CNBC on Friday.

"Things go downhill from here for us with King Abdullah's death. The next generation and others—while they talk a good game and a lot of happy talk toward the U.S. and what they want—what they really want is a very sustainable oil price, a higher one than I think we would like and can benefit from, and will work to do that," he said in a"Squawk Box"interview.

His viewpoint was echoed in part by other experts, who warned that Yemen developments and leadership in the regime are likely to make the situation fluid in the coming months.

Abdullah died Friday (Thursday EST) after effectively ruling the country for two decades. His half-brother, Crown Prince Salman, assumed the throne.

At the November OPEC meeting, Saudi Arabia refused to agree to production cuts. The move accelerated declines in crude prices, which are down about 60 percent from highs in June.

The Saudis want to "break the backs" of U.S. oil producers, and possibly those in Iran and Russia, as well, Kilduff said. The decision to keep oil production steady is largely seen as a bid by Saudi Arabiato protect its market share.

That shifts the responsibility to boost the price of oil through output cuts to other countries, particularly the United States, where oil production has increased about 50 percent between 2008 and 2013.

Brendan Smialowski | AFP | Getty Images

All eyes will be on what happens to those U.S. producers over the next several months now that the United States has taken the mantle of the world's swing producer from Saudi Arabia, IHS vice chairman Dan Yergin told CNBC.

The new king faces not just plummeting crude prices—Saudi Arabia is the world's largest oil exporter—but the potential for war in Yemen, its southern neighbor. The U.S.-aligned government in that country collapsed on Thursday as Shiite rebels from the north occupied much of the capital city, Sanaa.

The development increases the sense of anxiety and tension in the region and highlights the geopolitical risk there, Yergin said on "Squawk Box."

"What's been remarkable about the oil price—a year ago you had a lot of geopolitics in the price. Now there's no geopolitics in the price, but I think some of that may come back," he said.

As for internal stability, Abdullah went to lengths to ensure a smooth transition of power, but he made one unorthodox choice in his deputy crown prince, who has now become first in the line of succession, said Ian Bremmer, president of the Eurasia Group. Crown Prince Muqrin is capable but lacks tribal support, Bremmer said on "Squawk Box."

One thing to watch over the short to medium term is whether King Salman decides to replace Muqrin and bring in more loyalists.

"That would be a fairly big deal, and he would be able to do it without a lot of backlash," Bremmer said. "It could lead to a more cohesive and probably more reformist-oriented set of policies in Saudi Arabia."

Saudi Arabia can hold its share of the oil market at current prices through the end of 2015 and into 2016, Bremmer said. However, he thinks its leaders will budge on production cuts in the coming months because the economy is so dependent on oil revenues.

Even if Saudi decisionmakers had been thinking about taking some oil off the market in the near term, they must now wait as the country focuses on mourning its deceased leader.

"That's not going to get you more than a month, and beyond that, I think that the Saudis are going to be one of a few pieces that should be taking a little bit of oil off the markets from the Middle East," Bremmer said.

Former U.S. Ambassador to Saudi Arabia Chas Freeman said the Saudis can deal with the pain inflicted by its own policy for several years, noting that the country has hundreds of billions of dollars in foreign exchange reserves. The official figure from the World Bank is $737 billion as of 2013.

"I think the pain is real, but the determination to see this out, preserve and gain market share, squeeze out new sources of energy so that Saudi Arabia's patrimony is not dissipated, all of this is very real," he said in a "Squawk on the Street" interview.

There is currently no indication of disagreement in the kingdom over the strategy of riding out low prices, he said.

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